Method and apparatus for seismic prospecting



Nov. 16, 1937. s. A. SCHERBATSKOY ET AL 2,099,536

METHOD AND APPARATUS FOR SEISMIC PROSPECTING Filed Feb. 27, 1937 4Sheets-Sheet 1 D 33 W E? 3 a i D C: J

\NV EN TORS Nov. 16, 1937. s. A. SCHERBATSKOY ET AL 2,099,536

METHOD AND APPARATUS FOR SEISMIC PROSPECTING Filed Feb. 27, 1937 4Sheets-Sheet 2 d2 5 R E Q d B a m E FIG. 8

,Z'nvenZors.

Nov. 16, 1937. s. A. SCHERBATSKOY ET AL 2,099,536

METHOD AND APPARATUS FOR SEISMIC PROSPECTING Filed Feb. 27, 1957 4Sheets-Sheet 5 lNVENTORS 54% A. dwlwal Nov. 16, 1937. s. A. SCHERBATSKOYET AL 2,099,535

METHOD AND APPARATUS FOR SEISMIC PROSPECTING Filed Feb. 27, 19s? 4Sheets-Sheet 4 zoz if. I06

\NVENTORS A. Ma/al W Patented Nov. 16, 1931 PATENT OFFICE METHGI) ANDAPPARATUS FOR SEISMIC PROSPECTING Serge Alexander Scherbatskoy and JacobNeufeld, Tulsa, Okla, assignors to Engineering- Laboratories, Inc.,Tulsa, Okla., a corporation of Oklahoma Application February 2'7, 1937,Serial No. 128,264

64 Claims.

Our invention relates to seismic recording system and more particularlyto systems used for seismological exploration and provides a new andimproved method for receiving and recording seismic vibrations and thelike.

Seismological exploration consists in surveying the geological structureof the subsurface and determining ,the depths and slopes ofsubsurfacestrata with a view towards locating formations valuableminerals.

One of the methods of determining the subsurface strata comprisescreating earth vibrations y detonating an explosive at or near thesurface 1 of the earth and producing seismograms, i. e. graphicalrecords of vibrations after they have been influenced by variousgeological strata and V returned to the surface of the earth. In gen--erating earth vibrations a great many oscillations are set up. Some ofthese vibrations are valuable in the art of seismological explorationwhile others have an interfering effect and obscure the seismograms andmake the results diflicult to interpret. A

More specifically our invention relates to imwherein the waves reflectedfrom certain geo- 4 logical strata difiering in physical qualities fromadjacent strata are utilized. This method is well known in the art underthe name of reflection seismic method.

The reflection seismic methodcomprises the determining of the timeinterval required for a seismic wave to travel from the point of origintion being surveyed and back to the surface of the earth afterreflection from the subsurface formation. This time interval isdetermined by means of a seismogram which contains the initial signalcoincident with the explosive detonation and a record of identifiablereflected waves which are usually partly masked and partly obscured bythe interfering refracted, diffracted and direct waves. Due to therelative indeterminacy of the reflected waves considerable 'difiicultywas experienced in the prior art in the proper interpretation of theseismographic records and in many instances it was not possible toindicat'e positively the time at which reflected waves arrived at thesurface.

It is therefore the purpose of the present invention-to eliminate theinconveniences of the prior art and to produce a novel method and meansfor producing seismographic records in which the determinacy of thereflection points favorable to the accumulation of oil and otherprovements in seismic methods of exploration of the disturbance down tothe subsurface forms.

will be considerably increased. Thus the calculations employing theinterval of time between the detonation and the time of arrival of thereflected waves, are therefore accurate and it is possible to obtainsubstantially the exact depth of the subterranean beds at the points ofreflection.

It is another purpose of our invention to provide an apparatus which maybe effectively set to recognize and to reproduce in a visual form theenergy relationships involved in the reception of seismic waves.

A further purpose of the invention is to improve the method ofidentifying waves caused by the reflected energy.

A further purpose of our invention is to provide a means for recordingthe energy content of an earth particle participating in the groundmotion.

A further purpose of our invention is to provide a method and a meansfor translating the damped sinusoidal motion which characterizes seismicwavesinto a. substantially steady motion.

A further purpose of our invention is to reduce the number ofoscillations in a seismographic record and thus improve its clarity andlegibility.

Further purposes appear in the specifications and in the claims.

Our invention involves both the structure and the method subjectsmatter.

In the drawings we are illustrating certain features involving theprinciple of our invention and are showing three embodiments thereofwhich have been chosen in view of their simplicity in operation andconvenient illustration of the principles involved.

Figures la and 1b are intended to assist in the proper understanding ofthe invention. They contain diagrams representing graphically theeffects caused by the dropping of a weight from an appropriate heightupon the surface of the earth.

Figures 2a and 2b contain diagrams representing graphically the effectscaused by the dropping of two weights separately, at two successiveininstants.

Flgure 3 is a diagrammatic layout of a complete mechanism for practicingthe invention and shows the arrangement and functions of its variousconstituents. In thisfigure electrical connections are for convenienceindicated by single lines.

Figure 4 shows wiring diagrams of certain parts of Figure 3.

Figure 4a shows a modified fragment of Figure 4.

Figure 4b shows another modified fragment 0 Figure 4.

Figure 5 represents a seismographic record exthe inconveniences of theprior embodiment of the In order to explain certainfeatures of thepresentinvention reference is made to Figures 1a, 1b, 2a, 2b whichreproduce underidealized conditions some aspectsinvolved in thepropagation of seismic waves.

Figures 1a, 1b representthe eflectof dropping a weight from a certainheight upon the earth at a given location and of recording the resulting earth motion at another location. Figures 2a, 2b represent theefiect of dropping two weights at two successive instants and ofrecording the resulting earth motion at the referred locations. I Therecord of the motion of the earth in the first experiment is given inFigure 1a and Figure lb. Figure 1a represents graphically thedisplacement function a(t) of an earth particle in the wave motion. eordinatea represents the displacement of the earth particle from itsneutral position and t represents the time variable. The value t1corresponds to the instant at which the weight was dropped.

By inspecting Figure 1a it is observed that the surface of the earthwhen suddenly subjected to an impact caused by' dropping a weight is setin an oscillatory motion roughly resembling a damped sinusoid. i

During this oscillatory motion each earth particle possesses a certainamount of potential energy expressed by the formula:

. c (aEa(t) represents the displacement of the par-- ticle from itsneutral position at any instant t and s is the coeflicient ofelasticity; and a certain amount of kinetic en'ergy expressed by the.formula:

da da(t) E7 dt represents the rate of change of the displacement withrespect to the time or the velocity of the particle at any instant t and'm is the mass of the particle.

Then the total energy E(t) of the particle at any instant t is expressedby the formula:

1 1 da 2 E(t) 88 (3) During the oscillation of the referred earthparticle the value of the energy E(t) does not remain constant; part ofit dissipates itself in the form of heat and part of it is continuouslytransmitted in the form of a wave to the neighboring particles to whichit communicates the oscillatory motion. Thus upon receiving an initialimpulse the energy of the earth particle. rises '1 suddenly to a certainvalue and after the impulse the energy slowly decays. Figure 1billustrates qualitatively the energy decay of the particle. Theordinates E. represent the energy and energy E of the earth particle atany instant t.

Comparing Figure lawith Figure 2a and Figure 1b with Figure 2b it isobserved that the segments of the respective curves corresponding to thetime intervarbetweenthe instants'ti and t: are substantially alike incharacter and after the instant is acertain departure may be noticedbetween Figure 1a and Figure 2a and between Figure lb and 2brespectively. It is observed that this departure is more noticeablebetween Figures 1?) and 2b than between 1a and 2a and consequently .theinstant t2 corresponding to the 3 additional energy contribution is moredeterminate in Figure 2bthan Figure, 2a. In Figure 2a the function E(t)changes its slope at the instant t2 whereas in Figure 1b the oscillatorycharacterof the curve is'altered.

The two experiments described above approximate to some extentconditionsoccurring when; an explosive is buried in the earth and subsequentlydetonated. At theinstant of explosion a sudden impulse is generated andvarious unique and well known wave paths are created between the centerof the explosion and the given locality at which the earth motion isrecorded. Some of 1 these paths are directed along the surface of theearth, the other paths go downward so that the impulse encounters asuccession of simple strata at which it reflects or retracts itself andis returned to the surface of the earth. Thus the original impulsecreated by the explosion divides itself .into a plurality of impulseswhich travel along different paths in form of wave trains having variousvelocities and arrive to the given locality one after another insuccession and impress themselves on the recorder in form of a complexoscillatory motion. Thus the motion of the earth at the referred pointresults from a superposition of several wave trains each of thembringing its own energy contribution to the recorder. Since the effectof each impulse is somewhat analogous to the effect of dropping theweight, the effect resulting from producing the explosion may becompared with the effect resulting from the successive dropping ofseveral weights at several succeeding instants.

The analogy between the successive'dropping of weights and the arrivalof the successive wave trains caused by a dynamite detonation cannot bedrawn so as to include all details. The inspection of Figures 1a, 1b,2a, 2b, shows, however, that by studying the energy relationship ratherthan the actual motions it is easier to determine certain importantinstants at which the arrival of successive wave trains occur.

It should be noted that the purpose of geophyse ical Seismologicalrecording, as generally used, is not to study the actual ground motionsbut to determine certain instants at which the reflected waves arrive atthe surface of the earth and cause certain changes in the groundmotions. The method used in the prior art consisted in examining recordsof the actual ground motion and in deriving from them informationconcerning the occurrence of the reflection instants. The

ground motion results from the superposition of two effects, one ofwhich is caused by reflected waves and the other resulting from theprevious contributions due to direct, refracted waves and 'to thenatural oscillations of the earth. The

proper interpretation of the records consists in identifying thereflected waves which are partly masked. and covered up by other waves.Since all of the component waves produce oscillatory motions which aregenerally alike in character it is extremely difficult to separate thewaves on the record.

We are therefore introducing a new method in the seismologlcalgeophysical prospecting art, and

instead of actual ground motion we are recording the energy valuescaused by the arrival of seismic waves. It will be observed that in ourmethod the various component waves do not impress themselves on therecord in the form of oscillatory curves but produce steadily increasingor decreasing curves expressing the corresponding energy variationscorresponding to the motion of the earth.

One of the methods for recording energies involved in the earth motionis represented schematically in Figure 3. Referring now moreparticularly to this figure, rectangular blocks representdiagrammatically various system ,parts that 30 will be described indetail when reference is made to the subsequent figures and having thefunctions described below.

Blocks designated by letters G1, G2, Ga, represent geophones which areused for converting 5 earth vibrations into corresponding electricalvibrations.

A geophone includes usually a simple dynamical system characterized byan inertia coefficient m, friction coefficient e, resilience coem- 40cient bl and which is adapted to translate the motion of the earth intoa relative motion of two masses. The motion of the earth can berepresented by a function a(t) which gives the displacement of a givenearth particle from its 45 neutral position at any instant t, while therelative motion of two masses can be expressed by the function 11(t)which gives the distance between these two masses at any instant t. Theequation describing the motions involved can be 5? The function a(t)resulting from the earth motion shall be designated as the inputfunction while the function z/(t) resulting from the motion of thesystem shall be designated as the output and bad) in the Equation (4)can be made neg ligible when compared with the terms and d a( t) dt andconsequently the Equation (4) will be substantially equivalent to theequation:

d y(t) d a(t) m as m as (5) whence y( and the output function of thesystem will represent substantially the displacement of the earthparticles.

By selecting the constants of ,the system so as to make its naturalfrequency as high as possible 7 (by increasing the value of b) the termsand the output function of the system represents substantially theacceleration of the earth particles.

It is therefore obvious that the relation between the output functiony(t) and the input function a(t) as expressed by the Equation "(4) is ofsuch a nature that by selecting properly the constants of the system theoutput function may represent either the displacement or theacceleration of the earth particles or some other function dependingupon the earth motion.

In this particular embodiment we prefer to use a geophone of theGalitzin type in which the relative motion ,1; (t) of two masses is usedto generate an electromotive force substantially proportional of theirrelative velocity.

The outputs of geophones G1, G2, G3, are individually amplified by meansof suitable electronic arrangements contained in blocks A1, A2, A3. The

blocks A1, A2, A3, are individually connected to 7 electric filters F1,F2, F3. The purpose of the electric filters is to eliminate certainundesirable frequencies from the record of the earth oscillations. Themost predominant low frequency oscillations occurring in the earth(commonly knownas ground roll) are of the frequency range of about 10-20cycles per second and are due to waves that propagate themselves along.the surface of the earth. The filters F1, F2, F3 attenuate frequenciesbelow cycles per second and among others the ground roll frequencies andpass the frequencies above 30 cycles which include waves resulting fromreflected, refracted and diffracted paths.

Consider now the various instrumental steps associated with the geophoneG1, followed by the amplifier A, and filter F1. Let the output voltageof the filter F1, at any instant be designated by a function A10). Thefunction A1(t) represents largely those frequency components of thegeophone output which exceed 30 cycles per second and consequentlyrepresents mainly the contribution due to reflected, refracted, anddiffracted waves and is characterized by a relative absence of theground roll effects.

The voltage Aiit) delivered by the filter F1 is applied to a block 11and is also applied to a block S12. The block I1 represents a circuitarrangement for performing the process of integration electrically i. e.the block receives across its input terminals the voltage A10) anddeliver across its output terminals a voltage proportional to Kama:

proportional ,to

Kama:

and the block S11 delivers across its output terminals a voltagerepresented by the function.

(where K1 is the corresponding coefiicient of proportionality) Since thefunction Ai(t) represents the velocity of an earth particle, theexpression K2[A1(t)dt] represents the kinetic energy, while theexpression 4 Lame: corresponds to the displacement and.

to the potential energy.

In order to represent the kinetic energy and the potential energy on,the same scale the coefiicient K2 must correspond to' the mass of theoscillating particle and the coemcient K1 to the coefflcient ofelasticity. It is well known that:

K. where f is the natural frequency or the earth particle when displacedfrom its natural position. The most predominant frequency appearing inthe seismic records is subsequently equal to 48 cycles and it is assumedthat it represents the natural frequency of an oscillating earthparticle. Consequently a is usually taken in the neighborhood of 48cycles and the formula determines the ratio Ki/Ka necessary for,the'proper calibration of the blocks Sn and S12.

In such a manner we have provided means for producing across the outputterminals of the block Sn a voltage representing the potential energyand across the block $12 a voltage representing the kinetic energy of anearth particle participating in the ground motion. These two are thencombined at d1 in such a manner that the voltage impressed on therecorder R is the sum of their individual voltages.

The recorder R contains galvanometers which ,are adapted to respond tothe voltage applied across its input terminals and cause beams of lightto produce photographic records on the moving film in a manner wellknown in the art. The photographic record thus produced representsaooaoae the variation in the energy content of an earth particle themotion of which is detected by the geophone G1.

In a similar manner the motion of the earth particles detected by thegeophones Ga and G: causes corresponding voltages to be amplified and tobe forwarded to the filters F2 and F3 respectively. The output offilters F2 and F are subjected to the same instrumental steps as thevoltage delivered by F1, and the arrangementincluding blocks Fr, In,S22, S21, R as well as. the

arrangement including blocks F3, 13, S32, S31; R.

is similar to the arrangement containing F1, I1, S12, S11 as it is shownclearly in the schematic diagram of Figure 3.

The blocks 12 and I3 are similar in their structure and operation to theblocks I1. Sn and 8:1 are similar to S11, S22 and S32 are similar toS12.

' Accordingly the energy contents of earth'particles the motion of whichis detected by geophones G2 and G3 respectively impress themselves onthe photographic record contained in R in the same manner as the energydetected by the geo- A wiring diagram of the arrangement included inblocks I1, S11 and S12 is shown in Figure 4. Referring now moreparticularly to this figure, numerals I8 and II represent the outputterminals of the filter F1 (shown in Figure 3). 'Across the terminals I8andII is inserted a potentiometer consisting of a resistor I2 providedwith a tap terminal I3. The terminals I8 and II are connected to theinput terminals I4 and 15 of an electrical network contained in therectangle I5. This network shall be designated hereafter as anintegrator. One of the output terminals I8 of the integrator isconnected to the negative terminal of the battery I8 while the otheroutput terminal II is connected to the grid 88 of thei electronic tube8|. The integrator I8 consists of a resistor 82 inserted between theterminals I and I1 and of a capacitor 83 inserted between the terminalsII and I8. The electronic tube 8I includes a plate 84, grid 88 andcathode 85. The cathode-85 is connected to the positive terminals'of thebattery. I8 while the negative terminal of the battery 18 4 is connectedto the plate 84 by means of two pa s one of which includes the primarywinding 88 82 and has its terminals connected to anodes 88 and 84 of arectifier tube 85. An appropriate resistance 85 is inserted between theanodes 88 and 84. The rectifier tube85 possesses two cathodes 81 and 88which are connectedthrough the resistor 88 to the midpoint 82 of thewinding 8|. A three electrode tube I82 is provided; which contains ananode I83, grid I84 and cathode I85. The grid I84 of the tube I82 isconnected to the cathodes 81 and 88 of the rectifier tube 85 directly,while the cathode I85 of the tube I82 is connected to the cathodes 81and 88 of the rectifier tube 85 by means of a path consisting of abattery I08 in series with a resistor 88. The plate I83 is connected tothe cathode I85 by means of a path consisting of a'primary winding ofthe transformer I88 shunted by the resistor I88 and in series withbattery 88 and with the battery I88.

The terminals I8 and II are connected one with another by means of anadditional path consisting of a resistor I I2 in series with theresistor I I8. The resistor H8 is shunted by the capacitor Ill in seriesvvl" .i the primary winding I I5 of a transformer H6. The secondarywinding II! of the transformer H8 is provided with a midpoint II8 andhas its terminals connected to anodes H8 to the positive terminals ofthe battery I08 while the grid I28 is connected directly to the cathodesI28 and I24 the rectifier tube I2I and the anode I28 is connecteddirectly to the anode I03 of the I electronictube I02 by means of acommon terminal I0'I. The secondary winding of the transformer I08possesses output terminals I I0 and III which are connected directly tothe recording instrument R. r

The operation or the device can be explained as follows:

Assume that the geophones G1, Ga, Ga (in Figure 3) are of the velocitytype and consequently the voltage A 1(t) delivered by the filter F1, (inFigure 3) corresponds to the velocity of the earth particles andrepresents mainly those components which are caused by the refracted,reflected,

and diflfracted wavesv and in which the contribution due to the groundroll has been substantially eliminated.

Referring now more particularly to Figure 4: the voltage A1(t) isapplied to the input terminals I0 and II across the resistor I2 andissubsequently transmittdto the input terminals I4 and I5 of theintegrator IS. The integrator I8 integrates the input function A1(t)electrically i. e. it delivers across its output terminals 11 and I8 avoltage which is proportional to JZAKOdt The manner in which the outputvoltage V t J;A1(t)dt is produced can be explained as follows:

Let C be the capacitance of the capacitor 83, t

R the resistance of the resistor 82 and i(t) the current flowing throughthe resistor 82. Assume also that the output terminal ll of theintegrator I5 .has been disconnected, from the grid 80 of the tube 8|.Consequently the same current i(t) flows through the capacitor 83 andthrough the resistor 82 and the relation holds true:

where p denotes the operator i a: (as used in the Heavisides operationalcalculus).

See Carson: J. R. Carson, Electric Circuit Theory I i and OperationalCalculus, McGraw-Hill Book Co., New York, N. Y., 1926. Following themethods of operational calculus the current-Kt) can be expressed asfollows:

P cR -|-1 And the voltage A2(t) across the capacitor 88:

By taking CR )')1 the following relation may hold with an approximationsatisfactory for practical purposes:

Ala =fiao) (12) which by using conventional notation maybe written as:

Consequently the expression (13) which represents the voltage drop'Aa(t) across the condenser 83 between the output terminals TI and I8represents the time integral of the input voltage Aid). The Relation(13) results from the assumption that PCR+1-pCR in the Expression (11)and the approximation obtained has been found to be satisfactory bytaking C equal to" l.

microfarad and R equal to 300,000 ohms.

The voltage A) delivered across the output terminals 11 and I8 oi theintegrator 15 is subsequently applied between the negative terminal ofthe battery I8 and the grid 80 of the triode 8!. The battery I9constitutes the grid bias of the amplifier M and has been properlyselected in order to make the amplifier characteristics substantiallyrectilinear. Consequently in the plate circuit of the amplifier 8I thereappears across the winding 86 a voltage which is substantiallyproportional to A201) and is magnified to an extent depending upon thecoefllcient of amplification of the tube 84.

This voltage is subsequently transmitted through the transformer 81 tothe anodes 83 and 84 of the rectifier tube 95 and causes a rectifiedvoltage proportional to |A2(t)| to appear across the output terminais92and I00 of the rectifier and to be subsequently applied between theterminals IIII of the battery I06 and the grid I08 of the tube I 02. Thetube I02 and the grid bias supplied by the battery I05 have been chosenin such a manner that the platecurrent of the tube varies substantiallyas the square of the voltage applied across the terminals I00 and IN.Accordingly, since a voltage proportional to |Az(t)[ has been appliedacross the terminals I08 and IOI the plate current of the tube I02 canbe expressed by the function; K1[Az(t) where K1 is the proportionalityfactor determined by the constants of the circuit.

The voltage A1(t) applied between the terminals I8 and II is alsotransmitted through the resistor II2 to a circuit consisting of aresistor H3 in parallel with the capacitor IN and the primary winding II5 of the transformer 0. We prefer to use the resistor II8 substantiallyequal to the resistor 89, the capacitor Ill substantially equal to thecapacitor 88 and the transformer II6 having substantially the samecharacteristics as the transformer 87. In such a manner we transmitacross the anodes H9 and I20 oi the rectifier I2I a voltage whichsubstantially reproduces the input voltage A1(t) This voltage produces'a rectified current flowing between the terminals H8 and I26 and causesa voltage drop across the resistor I25. The voltage derived fromthe'resistor I is in turn applied between the negative terminal of thebattery I3I and the grid I29 of the tube I21.

The tube I21 and the grid bias supplied by the battery I8I have beenchosen in such a manner that the plate current of the tube variessubstantially as the square of the voltage applied across the terminalsIM and I28. Accordingly, since a Voltage proportional to Aid) has beenapplied across the terminals IN and I20, the plate current of the tubeI21 can be expressed by the function: K:[A1(t) where K: is theproportion- It will be observed-that the term K1[Az(t) is proportionalto the potential energy of an earth particle, the term K2[A1(t) l isproportional to the kinetic energy and the respective values K1 and K2are chosen in such amanner that the Expression (14) represents the totalenergy of the earth particle. Assuming that there is no leakage throughthe primary winding of the transformer I08 we may consider that thecurrent expressed by the Formula (14) passes entirely from the point I0!into the resistor I09 and causes across the terminals of this resistor avoltage drop which is substantially proportional to the Expression (14)and consequently represents the total energy of the earth particle. Thisvoltage drop is subsequently transmitted through theinput terminals H0and III to the recording apparatus R in which it impresses itself on astrip of photographic paper.

In such a manner we have provided means for automatically registeringthe energy content of an earth particle participating in the earthmotion. The geophones used for detecting the mo tion of the particle areof the velocity type.

Assume now that the geophones G1, G2, G3 (in Figure used to detect theearth vibrations are not of the velocity type but of the displacementtype and let the output voltage of the filter F1 (in Figure 3) berepresented by a function B0). (The displacement type geophones are wellknown in the art and one of them has been described by G. A. Ireland in"A Study of Some Seismometers published by the United States Dept. ofInterior, Bureau of Mines, Technical Paper 556, Washington, D. C.,1934.) The function B1(t) derived from the filter F1 represents thedisplacement of the earth particles and corresponds mainly to thosefrequency components which are caused by the refracted, reflected anddiffracted waves and which the contribution due to the ground roll hasbeen substantially eliminated. It will be observed then that thepotential energy of an earth particle will be represented. by K1[B1(t)]the kinetic energy by l (where K1 and K2 are properly chosenproportionality factors) and the total energy will be represented by theformula:

is shown diagrammatically in the rectangle I50 0i .nected from the tubeIII.

when it receives between .its input terminals I4 and I5 a certainvoltage it delivers across its output terminals 11 and I0 anothervoltage varying substantially as the derivative with respect to time ofthe input voltage. The derivator I50 consists of a capacitor I5Iinserted between the terminals 14 and ll of the resistor I52 insertedbetween the terminals 11 and I8.

The operation of the derivator can be explained mathematically asfollows:

Let 310.) be the function representing the voltage applied across theinput terminals 14 and 15 of the derivator I50, Bz(t) the functionrepresenting the voltage across the output terminals I1 and I8, C thecapacitance of the capacitor I5I, R the resistance of 1 the resistor I52and i(t) the current flowing through the capacitance I5I. Assume alsothat the output terminals 11 and 18 of the derivator I50 have beendiscon- Consequently the same current i(t) flows through the capacitanceI5I and through the resistance I59 and the following relation holdstrue:

Differentiating the Equation (16) we obtain:

Consequently the expression R i(t) which represents the voltage dropacross the resistor I52 between the output terminals 11 and I8 issubstantially proportional-to dB1(t) /dt which represents the timederivative of the input voltage across the terminals I1 and 10. TheRelation (19) results from neglecting the term R di/dt in the Equation(17) and the approximation obtained has been found to be satisfactory bytakmg C equal to 0.0003 microfarad and R equal to 10,000 ohms.

Consider new again Figure 4 and assume that the integrator I8 has beensubstituted by the derivator I50 (shown in Figure 4a.) and that thevoltage B1(t) has been applied across the input terminals I0 and 1|. Thevoltage delivered across the output terminals I1 and I0 of the derivatorI50 will be proportional -to dB1(t) /dt. This voltage is amplified in8i, rectified in and subsequently applied between the terminals IOI ofthe battery I00 and the grid I04 of the tube I02. Then the plate currentof the tube I02 can be expressed by the func-' I pulse.

the rectifier III and is subsequently rectified and applied between thepositive terminal of the battery HI and the grid I29 of thetube I21.Then the plate current of the tube I21 can be expressed by the functionK1[B1(t) where K1 is the corresponding proportionality factor determinedby the constants of the circuit.

The plate currents of the tubes I03 and I2! flow in the directionsindicated by the respective arrows toward the common point I01.Consequently the current flowing from the point I01 toward the resistorI09 is the equal of the sum of the respective plate currents and isrepresented by the energy Function (15) This current causes a voltagedrop across the resistor I09 and is transmitted to the recordingapparatus R. In such a manner we have provided means for theregistration of energy when the geophones used for detecting the earthmotion are of the displacement type. t

In order to illustrate the advantages of our invention we have shown twoseismograms in Figures 5 and 6. The seismogram of Figure 6 has beenobtained by means of the arrangement of Figure 4 and represents theenergy variations recorded in a given locality by means of a geophonesuitably placed and produced by the detonation of 1% pounds of dynamiteat 40 feet below the earth's surface. Figure 5 represents a conventionalseismograph record obtained by means of the arrangement of the prior artunder the same conditions (i. e. 1% pounds of dynamite, at 40 feet belowthe earth's surface and at the same spot as that of Figure 6). Since theconditions existing during the records of Figure 5 and Figure 6 are the,same the various reflected, refracted and direct waves have produced thesame motions at the geophones.

. Thephotographic records of the earth vibrations usually represent -arather complex oscillatory motion resulting from several wave paths.Upon a closer examination such a record may be thought to consist ofsegments each of which containing an oscillatory curve substantiallysinusoidal in character. Certain transition points may be found betweentwo adjoining segments such points determining a change in the characterof the oscillatory curve (1. e. change in frequency or amplitude of thecurve which roughly approximates a damped sinusoid). These transitionsoccur at certain critical instants corresponding to a new energycontribution resulting from the arrival of an additional wave im- In theenergy seismogram of Figure 6 the determinacy of the transition pointsis considerably increased and'one is able to identify the reflectionpoints a, b, c with a much greater facility and precision:

It will be observed that the number of oscillations in Figure 6 isconsiderably smaller than in Figure 5. This is due to the fact that to apurely sinusoidal displacement would correspond to a constant energyvalue and the energy function would be represented by a straight line.The motion of the earth is oscillatory and in the first approximation itmay be considered as a succession of sinusoidal fragments. To eachsinusoidal fragment would correspond a constant energy, 1. e. a straightlineand consequently the energy function may be considered as asuccession of straight line segments and to the beginning of eachsegment would correspond an instant at which the change of energy valuetake place.

From further comparison of Figure 5 and Figure 6 we see that the energyrecording'device possesses the property of translating the earth motionwhich is oscillatory and substantially sinusoidal into the energyvariations which are less subject to oscillations.

We have found that for the proper study of the earth motion it is notalways necessary to produce a record of the energy function and thatanother function which is capable of translating a substantiallysinusoidal motion into a substantially steady motion may be successfullyused for the proper identification of the reflection points. We wishtherefore to enlarge the scope of our invention and in furtherembodiments we are showing methods and means which are not directlyrelated to energy recording.

Consider again the modified arrangement of Figure 4 which includes thefeatures shown in 7 Figure 4a and assume that the voltage A1 (t)@ willappearacross the output terminals I I0 and l I I and will be recorded inR. It is obvious that the Expression (20) does not have any definitephysical meaning and does not represent the energy because the functionA1(t) corresponds to .the displacement and not to the velocity of theearth motion. It has been found, however that the record of the Function(20) presents certain obvious advantages and facilitates to a very greatextent the reading and the proper interpretation of the earthvibrations. This results not from the physical but from the mathematicalproperties of the Function (20) which permits to transform asubstantially sinusoidal function into a substantially steady function.

In order to illustrate the properties of the Function (20) let the inputvoltage across the terminals I0 and H be Ai(t) =Mi sin 21ft. Thecorresponding voltage across the output terminals H0 and III isrepresented by the Function which in the particular case when A1(t) =M1sin 21rft will be reduced to the value M1 (when the relation (S) istaken into account). In such a manner we have provided means fortransforming a pure sinusoidal voltage into a steady voltage and weconsider this to be of particular importance in the recording of seismicwaves.

In the actual interpretation of the seismic records we are interested inidentifying the reflection points corresponding to the change of energycontent of the oscillating earth particles and consequently instead ofstudying the energy function directly we may study the derivative of theenergy function in order to identify the reflection points.

A record of the derivative of the energy function maybe obtained byconnecting the output terminals i I0 and II I of the device shown inFigure 4 to the derivator 200 (shown in Figure 4b). The derivator 200(similar to the one designated by I50 in Figure 4a) has its outputterminals 20l and 202 connected to the recorder and it includes acapacitor 203 inserted between the terminals I I0 and 2M and a resistor204 inserted between the 'will be subsequently recorded in R.

Mathematically, the-derivative of the energy function will be expressedas follows:

and will consist of a product of two terms: the term 2Ai(t) and the termIn the study of the earth vibrations 531318186.

tory results may be obtained in some instances by studying only one ofthe above terms entering in the expression of the derivative of theenergy function and namely the term K f A (t)dt+K 2 22 The Expression(22) is capable of translating a sinusoidal motion of the frequency w(determined by the Formula (8)) into a substantially steady motion,because when substituting sin wt in'(22) this expression is reduced tozero. Consequently the Expression (22) possesses certain propertieswhich are somewhat similar to those of the Expression (20) and iscapable of translating a substantially sinusoidal motion into asubstantially steady motion thus increasing'the determinacy of thereflection points in the manner indicated above. a

We are therefore proposing another embodiment of our invention showndiagrammatically on Figure 7 and intend to produce a photographic recordof the Expression (22). The arrangement shown comprises an integratorand a derivator which are respectively connected to the input terminals10 and 1!. The integrator (similar to the one included in thedottedrectangle 16 of Figure 4) includes a resistor I60, one terminal ofwhich is connected to the input terminal 10 and the other terminal ofwhich is connected to the input terminal 1| through the capacitor I6I.The output terminals I62 and I63 of the integrator are connected to thenegative terminal of the battery I64 and to the grid I65 of the tube I66respectively. The derivator (similar to the one contained in the dottedrectangle I50 of Figure 4a) includes the capacitor I65 one terminal ofwhich is connected to the input terminal 10 and the other terminal ofwhich is connected to theinput terminal 1I through the resistor I66. Theoutput terminals I63 and I61 of the derivator are connected to thenegative terminal of the battery I68 and to the grid I69 of the tube I10respectively.- The negative terminal of the battery I64 has a commonterminal I with the negative terminal of the battery I68 and the plateI12 of the tube I66 is connected to the plate I13 of the tube I10through a common terminal I14. The terminals HI and I14 are connectedone with another by means of a path which includes a battery I15 inseries with a resistor I16 and the resistor I16 is shunted by a primarywinding I11 of the transformer I18. The secondary winding of thetransformer I18 is connected through the output terminals no and m tothe recorder R.

The operation of the device can be explained as follows: Assume that thegeophones used to detect the earth vibrations are of. the velocity typeand let the output voltage of the filter F1 (in Figure 3) be representedby the function Ai(t). The function A1(t) represents the velocity of theearth particles and corresponds mainly to those frequency componentswhich are caused by the refracted, reflected and diffracted waves and inwhich the contribution due to the ground roll has been substantiallyeliminated. The voltage A10?) applied across the input terminals 10 andH will be transmitted to the integrator and to the derivator. Across theoutput terminals I62 and I63 of the integrator there will appear avoltage varying substantially as J'Ai(t)dt while across the outputterminals I61 and I63 of the derivator the voltage will varysubstantially as the function These voltages are subsequently amplifiedby the tubes I66 and I61 so that the plate current of the tube I66 isexpressed by the function directions indicated by arrows toward thecommon terminal I14. Thus the current flowing from the terminal I14toward the resistor I16 is equal to the sum of the respective platecurrents and is expressed by (22). Assuming that there is no leakagethrough the primary winding I11 of the transformer I 18, we may considerthat the current expressed by the Formula (22) passes entirely fromthepoint I14 into the resistor I16 and causes across the terminals ofthis resistor a voltage drop which is substantially proportional to theExpression (22). This voltage is subsequently transmitted to the outputterminals H0 and III and to the recorder R. Thus we have provided meansfor automatically registering the instantaneous value of the Expression(22) For the reasons which have been explained above the record of thisexpression increases the determisent the output of the geophone, thesymbol d' /dt denotes difierentiation of the order n, the symbol d-/dtdenotes integration of the order m; k is a positive or negativeinteger, r is an odd integer, K1 and K2 are properly chosen components.Then by using means explainedabove we can register the expression:

and to observe the obtained record for the points of reflection. It isnoted that if f(t)= A(t) k=0, r=1 the above expression can be made torepresent the Formula (20).

In a similar manner we may consider a function representing the timederivative of the Expression (23), i. e.

displacement .geophonenof the type described in.

the above referred to article by G. A. Ireland and Gv represents avelocity type geophone which may be of the Galitzin type. ,The outputsof geophones Go and Gv are transmitted to the respective filters Fe andFv which eliminate the eflects resulting from the grouhd rolldisturbance. Consequently there appears across the output terminals offilters Fn and Fv voltages Aid) and 131G) which correspond respectivelyto the displacement and to the velocity of the ground motion andrepresents mainly the frequency components dueto the reflected,refracted and. diffracted waves and are characterized by a relativeabsence of ground roll efiects. The voltages A1(t) and Bid) aresubsequently squared in the squaring devices Sn and Sv similar to thoseindicated by S11, S12, S21, etc. in Figure 3 and their output is addedand recorded in the recording apparatus R. It is obvious to thoseskilled in the art that the squared voltage delivered by Sn representssubsequently the potential energy of the oscillating earth'particleassociated with the earth motion and the squared voltage delivered by Svrepresents the kinetic energy. Consequently the voltage recorded in Rrepresents the total energy of the earth particle.

It is therefore apparent that we have provided a novel method and meansfor producing seismographic records in which the determinacy of thereflection points will be considerably increased. The calculationsemploying the interval of time between the time of detonation and thetime of reception of the reflected waves, is, therefore accurate and itis possible to obtain substantially the exact depth of the subterraneanbeds at the points of reflection.

When reference is made to a geophone, it is intended to include anyelectromechanical transducer which transforms one type of vibratorymotion into another, and to designate instruments commonly known asgeophones, seismographs, seismometers, ,seismoscopes, microphones,detectors, magnetophones, etc.

The expression recorder is intended to include any transducer which,when acted upon by earth vibrations, produces a registration of the saidvibrations, such a transducer may be of the mechanical,electromechanical or other type,

and may consist of and include in its construction means for receiving,detecting, translating, transmitting, amplifying, indicating, andregistering the said vibrations, or means for doing any of these thingsin addition to indicating or recording.

The expression "at the earth's surface is intended to include arelatively thin stratum of the earth close to its surface.

When reference is made to a derivative of a magnitude or an effect it ismeant to designate a magnitude or an effect which has been obtained froma given magnitude or a given eiiect and which varies according to afunction which is a time derivative of the function expressing thevariation of the given magnitude or of the 5 given effect, such as atime derivative of the first order, or of the second order, or of thefirst order combined with the second order or of any higher order, ortwo or a plurality of derivatives combined in any way.

When reference is made to a "derivator it is meant to designate one ortwo or three, or a plurality of derivators arranged in an appropriateway, it will be'understood that one derivator only may be used, or two,or any plurality of derivators. r.

When reference is made an integrai oi a V which is an integral of thefunction expressing the variation of the givenmagnitude or eflect, suchas a time integral of the first order or oi the second order, or of thefirst order combined with the second order or any higher order, or twoor a plurality of integrals combined in any way.

When reference is made to an "integrator" it is meant to designate oneor two or three or a plurality of integrators arranged in an appropriateway.

When reference is made to the square of a magnitude or of an efiect itis meant to designate a magnitude or an effectwhich has been obtainedfrom a given effect and which varies according to a function which isthe square of the function expressing the variation of the givenmagnitude or efiect.

In view of our invention and disclosure variations and modifications tomeet individual whim or particular need will doubtless become evident toothers skilledin the art, to obtain part or all of the benefits of ourinventionwithout copying the structure shown, and we, therefore, claimall such in so far as they fall within the reasonable spirit and scopeof our invention.

,We claim:

1. The method of seismic surveying which comprises creating adisturbance below theearths surface, receiving the several waves thusformed, translating these waves into electrical vibrations, applying theelectrical vibrations to an element responsive to their magnitude andtheir derivative, recording the output of the said element.

2. The method of seismic surveying which comprises creating adisturbance below the earths surface, receiving the several waves thusformed, translating these waves into electrical vibrations deriving aneffect substantially proportional to the square of the vibrations,deriving another effect substantially proportional to the square of therate of change of the vibrations, adding the two eifects, and recordingthe sum.

3. The method of seismic surveying which comprises creating adisturbance below the earth's surface, receiving the several waves thusformed, translating these waves into electrical vibrations, producing anelectrical effect depending upon a derivative of the electrical Vlbl'flrformed, translating these waves into electrical vibrations, producing anelectrical efiect depending upon the magnitude of the electricalvibrations and upon the derivative of the said magnitude, recording theelectric efi'ect.

5. The method of seismic surveying which comprises creating adisturbance below the earths surface, receiving the several waves thusformed, translating these waves into electrical vibrations, producing anelectric efiect depending uponthe magnitude of the electrical vibrationsand the integral of the said magnitude, recording the electric efiect.6. The method of seismic, surveying which comprises creating -adisturbance below the earths surface, receiving the several waves thusformed, translating these waves into electrical vibrations, producing anelectric effect depending upon a derivative and an integral of themagnitude of the electrical vibrations, recording the electric efiect.

'7. The -method of seismic surveying which comprises creating adisturbance below the earths surface, receiving the several waves thusformed, translating these waves into electrical vibrations, producing anelectric efiect dependent upon the magnitude of the electricalvibrations, producing an electric .efl'ect dependent upon the timederivative of the said magnitude, adding the two eflfects.

8. The method of seismic surveying which comprises creating adisturbance below the earths surface, receiving the several waves thusformed, translating these waves into electrical vibrations, producing anelectric effect depending upon the magnitude of the electric vibrations,producing an electric efiect depending upon the time integral of thesaid magnitude, adding the two efi'ects.

9. The method of seismic surveying which comprises creating adisturbance below the earths surface, receiving the several waves thusformed, translating these waves into electrical vibrations, producing anelectrical efiect depending upon the rate of change of the electricvibrations, producing an electric efiect depending upon the timeintegral of the electric vibrations, adding the two efiects.

10. The method of seismic surveying which comprises creating adisturbance below the earths surface, receiving the several waves thusformed, translating these waves into electrical vibrations, producing anelectric effect dependent upon the square of the magnitude oftheelectrical vibrations, producing an electrical effect dependent uponthe square 'of the time derivative of the said magnitude, adding the twoefiects. v

11. The method of seismic surveying which comprises creating adisturbance below the earths surface, receiving the several waves thusformed, translating these waves into electrical vibrations, producing anelectric effect dependent upon the square of the magnitude of theelectric vibrations, producing an electric effect dependent upon thesquare of the time integral of the said magnitude, adding the twoefiects.

12. The method of seismic surveying which comprises creating adisturbance below the earths surface, receiving the several waves thusformed, translating these waves into electrical vibrations, producing anelectrical efiect depending upon the square of the time integral of theelectrical vibrations, producing an electrical efiect depending'upon thesquare of the derivaaoaassc tive of the electrical vibrations adding thetwo effects.

13. In the method of seismic surveying by creating a disturbance in theearth, receiving the several waves thus formed at a convenient distancefrom the center of the disturbance, the step consisting in translatingthe said waves into a varying electrical efiect consisting ofoscillations, the number of which is smaller than the.

number of oscillations in the received waves, recording the saidelectrical effect.

14. In the method of seismic surveying by creating a disturbance in theearth, receiving the several waves thus formed at-a convenient distancefrom the center of the disturbance, translating the said waves into anoscillatory current, deriving from the said oscillatory cur rent anothercurrent with a decreased number of oscillations, recording the saidderived oscillatory current and observing the record for points ofreflection.

15. In the method of seismic surveying by creating a disturbance in theearth, receiving the several waves thus formed at a convenient distancefrom the center of the disturbance, translating the said wave trainsinto a succession of damped electrical oscillations, the step whichconsists in translating each of the damped oscillations 'into asubstantially steady electrical eifect, recording the succession of thesaid'electrical effects.

16. The method of seismic surveying which I comprises creating adisturbance below the earths surface, receiving the several waves thusformed, translating these waves into electricaloscillations consistingof a succession of substantially sinusoidal fragments, transforming thesubstantially sinusoidal fragments into substantially unidirectionalfragments, thus increasing the determinacy of points separating thesefragments.

17. The method of seismic surveying which comprises creating adisturbance below the earth's surface, receiving the several waves thusformed,

translating these waves into electrical vibrations, producing avoltagevarying substantially according to a formula 2 K.l )l +K2[% wheref(t) expresses the said electrical vibrations K1 and K2 are properlychosen constants. recording this voltage.

18. The method of seismic surveying which comprises creating adisturbance below the earths surface, receiving the several waves thusformed, translating these waves into electric vibrations, producing avoltage varying substantially according to a formula KlI unMmMIg-QMTwhere f(t) expresses the said electrical vibrawhere ,f(t) expresses thesaid electrical vibrations,

K1 and K2 are properly chosen constants, recording this voltage.

aooasa'e 20. the method a: seismic surveying which comprises creating adisturbance below the earth's surface, receiving the several waves thusformed,

translating these waves into electrical vibrations, filteringcertainundesirable frequencies from among the'electrical vibrations,producing a voltage varying substantially according to a formula whereflt) expresses the electrical vibrations from which the undesirablefrequencies have been eliminated, K1 and K2 are properly chosenconstants, recording this voltage.

21. The method of seismic surveying which comprises creating adisturbance below the earth's surface, receiving the several waves thusformed, translating these waves into electrical vibrations, filteringcertain undesirable frequencies from among the electrical vibrations,producing a voltage varying substantially according to a formulamlrcorweu rweq where Kt) expresses the electrical vibrations from whichthe undesirable frequencies have been eliminated, K1 and K2 are properlychosen constants, recording this voltage.

22. The method of seismic surveying which comprises creating adisturbance below the earth's surface, receiving the several waves thusformed.

- translating these waves into electrical vibrations,

filtering certain undesirable frequencies among the electricalvibrations, producing a voltage varying substantially according to aformula where {(t) expresses the electrical vibrations from which theundesirable frequencies have been eliminated, K1 and m are properlychosen constants, recording this voltage.

23. In a system for'geological surveying, means for creating adisturbance in the earth, means for translating the waves resulting fromthe disturbance into electrical vibrations, means for creating anelectrical effect depending upon a time derivative of the magnitude ofthe electrical vibrations, means for recording the electric 'eflect.

24. In a system for geological surveying, means for creating adisturbance in the earth, a plurality of geophones conveniently placedat the earth's surface, which receive the waves resulting from the saiddisturbance and translate them into electrical vibrations, means forcreating an electrical efiect depending upon the magnitude of theelectrical vibrations and upon the time derivative of the saidmagnitude, means for recording the electric effect.

25. In a system for geological surveying, means for creating adisturbance in the earth, a plu-' rality of geophones convenientlyplaced at the earths surface, which receive the waves resulting from thesaid disturbance and translate them into electrical vibrations, meansfor creating an electrical effect depending upon the magnitude ofearth's surface, which receive the waves resulting from the saiddisturbance and translate them into electrical vibrations, means forcreating an an integral of the magnitude of the electric vibrations,means for recording the electrical effect.

27. In a system for geological surveying, means for creating adisturbance in the earth, a plur'ality of geophones conveniently placedat the earth's surface, which receive the waves resulting from the saiddisturbance and translate them into electrical vibrations, means forcreating an electrical eflect depending upon the magnitude of theelectrical vibrations, means for creating an electrical effect dependingupon the time derivative of the said magnitude,.means for adding andrecording the said efleots.

28. In a system for geological surveying, means of geophonesconveniently placed at the earth's surface which receive the wavesresulting from the said disturbance and translate them into electricalvibrations, means for creating an elecelectrical eiiect depending upon aderivative and for creating a disturbance in the earth, a plurality Vtrical effect depending upon the magnitude of the electrical vibrations,means for creating an electrical effect depending upon the time integralof the said magnitude, means for adding and recording the saidelectrical efiects.

29. In a system for geological surveying, means for creating adisturbance in the earth, a plurality of geophones conveniently placedat the earth's surface, which receive the waves resulting 'from the saiddisturbance and translate them into electrical vibrations, means forcreating an electrical eflect depending upon the derivative of themagnitude of the vibrations, means for creating an electrical efi'ectdepending upon the integral of the electrical vibrations, means foradding and recording the said effects.

30. Ina system for geological surveying, means for creating adisturbance in the earth, means for translating the waves thus producedinto electrical vibrations, means for producing a voltage varyingsubstantially as dKt) 2 a. lawman]:

where fit) represents the electrical vibrations, K1 and K2 are properlychosen constants, means for recording this voltage.

31. In a system for geological surveying, means for creating adisturbance in the earth, means for translating the waves thus producedinto electrical vibrations, means for producing a voltage varyingsubstantially as mldol s-mmrtedqa where j(t) represents the electricalvibrations, K1 and K2 are properly chosen constants, means for recordingthis voltage.

33. In a system for geological surveying, means for creating adisturbance in the earth, a plurality of geophones conveniently placedat the earth's surface, which receive the waves resulting from the saiddisturbance and translate them into electrical vibrations, filterseliminating certain undesirable frequencies among the electricalvibrations, and delivering a voltage varying with time t as a function{(t), means for producing a voltage varying substantially as where K1and K2 are properly chosen constants, means for recording this voltage.

34. In a system for geological surveying, means for creating adisturbance in the earth, a plurality of geophones conveniently placedat the earth's surface, which receive the waves resulting from the saiddisturbance and translate them into electrical vibrations, filterseliminating certain undesirable frequencies among the electricalvibrations, means for producing a voltage varying substantially as 2 K1i)l+ 2[ where j(t) is the voltage output of the filter, K1 and K2 areproperly chosen constants, means for recording this voltage.

35. In a system for geological surveying, means for creating adisturbance in the earth, a plurality of geophones conveniently placedat the earths surface, which receive the waves resulting from the saiddisturbance and translate them into electrical vibrations, filterseliminating certain undesirable frequencies among the electricalvibrations, means for producing a voltage varying substantially as d f tK1 (o+K2 fl where (t) is the voltage output of the filter, K1 and K2 areproperly chosen constants, means for recording this voltage. 36. Themethod of seismic surveying, which comprises creating a disturbancebelow the earths surface, receiving the several waves thus formed,translating these waves into electrical vibrations, producing a voltagevarying substanducing a voltage varyingsubstantially according to aformula dk 2 dk-i-r 2 1[a i- 2[ where j(t) expresses the electricalvibrations from which the undesirable frequencies have been eliminated,the symbol d /dt" denotes differentiation of the order n, the symbol (F/didenotes integration of the order m, k is a positiveor negativeinteger, 1' is an odd integer, K1

and K2 are properly chosen constants, recording this voltage.

38. In a system for geological surveying, means for creating adisturbance in the earth, means for translating the waves thus producedinto electrical vibrations means for producing a voltage varyingsubstantially as b 2 k+r 2 1[ 2[ JU)] where j(t) expresses the saidelectrical vibrations, the symbol d'Vdt" denotes differentiation of theorder n, the symbol .'Z'"/dt-" denotes integration of the order m, k isa positive or negative integer, r is an odd integer, K1 and K2 areproperly chosen constants, recording this voltage.

39. In a system for geological surveying, means for creating adisturbance in the earth, a plurality of geophones conveniently placedat the earth's surface, which receive the waves resulting from the saiddisturbance and translate them into electrical vibrations, filterseliminating certain undesirable frequencies among the electricalvibrations, means for producing a voltage varying substantially as 1: 2dH-r a K1[ (o] +K2[;, ,r(o] where f(t) is the voltage output of thefilters, the symbol dVdt denotes differentiation of the order n, thesymbol d- /dtdenotes integration of the order m, k is a positive ornegative integer, r is an odd integer, K1 and K2 are properly chosenconstants, recording this voltage.

40. The method of seismic surveying which comprises creating -adisturbance below the earth's surface, receiving the several waves thusformed, translating these waves into electric vibrations, producing avoltage varying substantially according to a formula where {(t)expresses the said electrical vibrations, the symbol d /dt denotesdifferentiation of the order n, the symbol d"/dtdenotes integration ofthe order m, k is a positive or negative integer, s is an even integer,K1 and K2 are properlychosen constants, recording the said voltage.

41. The method of seismic surveying which comprises creating adisturbance below the earth's surface, receiving the several waves thusformed, translating these waves into electric vibrations, filtering outcertain undesirable frequencies from the said electrical vibrations,producing a voltage varying substantially according to a formula wheref(t) expresses the filtered electrical vibrations, the symbol d ldtdenotes differentiation of the order n, the symbol d-'"/dt denotesintegration of the order m, -k is a positive or negative integer, s isan even integer, K1 and K2 are properly chosen constants, recording thesaid voltage.

42. In a system for geological surveying means for creating adisturbance in the earth, means for translating the waves thus producedinto electrical vibrations, means for producing a voltage varyingsubstantially as where the function ,f(t) represents the saidele'ctrical vibrations, the symbol d' /dt" denotes differentiation ofthe order n, the symbol d-"Vdf'" denotes integration of the order m, Itis a posi-' tive or negative integer, s is an even integer,

the said disturbance and translate them into electrlcal vibrations,electric filters eliminating certainundesirable frequencies among theelectrical vibrations means for producing a voltage varyingsubstantially as V where the function f(tl represents the of thefilters, the symbol d'vdt denotes differentiation of the order n, thesymbol d-"/dt" denotes integration of the order m, k is a positive ornegative integer, s is an even integer, K1 and K: are properly chosenconstants, recording the said voltage.

44. The method of increasing the determinacy of the reflection points ina record of the earth vibrations which consists in producing effectsrepresenting derivatives of the earth vibrations, combining andrecording the effects and observing the record of the combination of thederivatives for the points of reflection.

45. In combination with a geophone a filter, a derivator, means forsquaring the output of the derivator, means for squaring the output ofthe geophone, means for producing the sum of the said squared outputs,means for recording the sum.

46. In combination with a geophone, a filter, an integrator, means} forsquaring the output of the i integrator, means for squaring the outputof the geophone, means for producing the sum of the said squaredoutputs, means for producing the record of the sum.

47. In combination with a geophone, a filter, an integrator, aderivator, means for combining the output of the integrator and of thederivator, means for recording the combined output.

48. In combination with a geophone, a filter, an integrator, aderivator, means for adding the output of the integrator and of thederivator, means for recording the added output;

49. The method of seismic surveying which comprisescreatinga'disturbance in the earth, and recording the rate of change ofthe energy derived-from the disturbance.

50. The method of seismic surveying which comprises creating adisturbance in the earth, recording the rate of change of the energyderived from the disturbance and observing the record for the points ofreflection.

51. The method of seismic surveying which comprises creating adisturbance below the earth's surface, receiving the several waves thusformed, translating-these waves into electric vibrations, producing avoltage varying substantially according to a formula where f(t)expresses the said electrical vibrations, K1 and K2 are properly chosenconstants, recording this voltage.

52. The method of seismic surveying which comprises creating adisturbance below the earth's surface, receiving the several waves thusformed. translating these waves into electric vibrations, producing avoltage varying substantially according to a formula where j( t)expresses the said electrical vibrations, K1 and K2 are properly chosenconstants, recording this voltage.

53. The method of seismic surveying which comprises creating adisturbance below the earth's surface, receiving the several waves thusformed, translating these waves into electrical vibrations, filteringcertain undesirable frequen-' cies among the electrical vibrations,producing a voltage varying. substantially according to a where fit)expresses the electrical vibrations from which the undesirablefrequencies have been eliminated, K1 and K2 are properly chosenconstants, recording this voltage.

54. The method of seismic surveying which comprises creating adisturbance below the earth's surface, receiving the several waves thusformed, translating these waves into electrical vibrations, filteringcertain undesirable frequencies among the electrical vibrations,producing a voltage varying substantially according to a formula whereflt) expresses the electrical vibrations from which the undesirablefrequencies have been eliminated, K1 and K2 are properly chosenconstants, recording this voltage.

55. In a system for geological surveying, means for creating adisturbance in the earth, means for translating the waves thus producedinto electrical vibrations, means for producing a voltage varyingsubstantially as where f (t) represents the electrical vibrations, K1and K2 are properly chosen constants, meansfor recording this voltage.

56. In a system for geological surveying, means for creating adisturbance in the earth, means for translating the waves thus producedinto electrical vibrations, means for producing a voltage varyingsubstantially as where Kt) represents the electrical vibrations, K1 andK2 are properly chosen constants, means for recording this voltage.

57. In a system for geological surveying, means for creating adisturbance in the earth, a plurality .of geophones conveniently placedat the earth's surface, which receive the waves resulting from thesaiddisturbance and translate them into electrical vibrations, filterseliminating certain undesirable frequencies among the electricalvibrations, and delivering a voltage varying with time .t as a function{(t) means for producing a voltage varying substantially as where K1 andK2 are properly chosen constants, means for recording this voltage.

58. In a system for geological surveying, means for creating adisturbance in the earth, a plurality of geophones conveniently placedat the earth's surface, which receive the waves resulting from the saiddisturbance and translate them into electrical vibrations, filterseliminating certain undesirable frequencies among the electricalvibrations, means for producing a voltage varying substantially as wheref(t) is the voltage output of the filter, K1 and K: are properly chosenconstants, means for recording this voltage.

59. The method of seismic surveying which comprises creating adisturbance below the earth's surface, receiving the several waves thusformed, translating these waves into electrical vibrations, producing avoltage varying substantially according to a formula d z 2 2 AKIB- KQ]+K ho] where .f (t) expresses the said electrical vibrations, the symbold"/dt" denotes differentiation of the order n, the symbol d ldtdenotesintegration of the order m, k is a positive or negative integer, r is anodd integer, K1 and K2 are properly chosen constants, recording thisvoltage.

60. The method of seismic surveying which comprises creating adisturbance below the earth's surface, receiving the several waves thusformed, translating these waves into electrical vibrations, filteringcertain undesirable frequencies among the electrical vibrations,producing a voltage varying substantially according to a formulategration of the order m, k is a positive or negative integer, r is anodd integer. K1 and K2 are properly chosen constants, recording thisvoltage. 61. In a system for geological surveying means for creating adisturbance in the earth, means for translating the waves thus producedinto electrical vibrations, means for producing a voltage varyingsubstantially as desirable frequencies among the electrical vibra-'-tlons, means for producing a voltage varying substantially as k 3 k+r 2{m[%,I o] +K2[ /(o] where f(t) is the voltage output of the filters, thesymbol d"/dt" denotes difierentiation of the order n, the symbold-'"/dt-'" denotes integration of the order m, k is apositive ornegative integer, r is an odd integer, K1 and K: are'properly chosenconstants, recording this voltage.

63. In combination with a geophone a filter, a derivator, meansforsquaring the output of the derivator, means for squaring the outputof the geophone, means for producing the sum of the said squaredoutputs, means for producing the derivative of the sum, means forrecording the derivative.

64. In a combination with a geophone, a filter, an integrator, aderivator, means for combining the output of the integrator and of thederivator, means for producing a derivative of the com- .bined output,means for recording the derivative.

SERGE A. SCHERBATSKOY.

JACOB NEUFELD.

